Massless $AdS_2$ scattering and Bethe ansatz

We first analyse the integrable scattering theory describing the massless excitations of $AdS_2 \times S^2 \times T^6$ superstrings in the relativistic limit. The matrix part of the S-matrix is obtained in the BMN limit from the conjectured exact expression, and compared with known S-matrices with N=1 supersymmetry. A dressing factor, yet unknown for the complete theory, is here constructed based on relativistic crossing symmetry. We derive a Bethe-ansatz condition by employing a transfer-matrix technique based on the so-called free-fermion condition. This is known to overcome the problem of lack of a reference state. We then generalise the method to the massless non-relativistic case, and compare the resulting Bethe-ansatz condition with a simple massless limit of the one conjectured by Sorokin, Tseytlin, Wulff and Zarembo.